maths (F.4)

1. suppose the equation 2x(x-1)=k-5 does not have any real roots and k is an integer, Find the greatest possible value of k .

2x(x-1)=k-5
2x^2-2x-k+5=0

(2)^2-4(2)(5-k)<0
4-40+8k<0
8k<36
k<4
所以最大既k值係3...

(log2)^2+(log5)^2+(log4)(log5)
=(log2)^2+(log5)^2+(log2^2)(log5)
=(log2)^2+(log5)^2+2(log2)(log5)
= (log2+log5)^2
=(log10)^2
=1